Available online at www.sciencedirect.com ScienceDirect

Energy Procedia 69 ( 2015 ) 116 – 125

International Conference on Concentrating Solar Power and Chemical Systems, SolarPACES 2014 Wind loads on Linear Fresnel Reflectors’ technology: a numerical study

Q. Lancereaua,* , Q. Rabuta, D. Itskhokinea, M. Benmarrazea

a Solar Euromed, 3 avenue de la Découverte Parc Technologique, Dijon, F-21000,

Abstract

The wind effect on the Fresnel technology is one of the main design stresses for the metallic structure, primary reflectors, receivers and solar tracking system. Therefore, in order to quantify its impact and compare it to a more mature technology (the Parabolic Trough), a first study of the wind load on a Linear Fresnel Reflector (LFR) collector with an air-stable absorber tube receiver (with protective cover glass) has been undertaken. The drag, lift and momentum coefficients of the receiver and primary reflectors have been calculated using a bi-dimensional CFD model based on the COMSOL Multiphysics® software. The impact of the transversal wind speed has been studied. Moreover, the interaction between the receiver and the primary reflectors has been quantified. Finally, a comparison to Parabolic Trough collectors has been made, which confirms the much lower wind load of LFR technology for an equal aperture area, and thus the much lighter structures required for resisting these wind loads and/or the larger operation range with respect to wind speed.

©© 20152015 The The Authors. Authors. Published Published by byElsevier Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer review by the scientific conference committee of SolarPACES 2014 under responsibility of PSE AG. Peer review by the scientific conference committee of SolarPACES 2014 under responsibility of PSE AG Keywords: Wind load; Linear Fresnel Reflector; Parabolic Trough

1. Introduction

Among all CSP technologies, Linear Fresnel Reflectors (LFR) technology is deemed a very promising solution, thanks to its design and installation simplicity [1,2], lower raw material use [1–3], cost attractiveness [1–4] and

* Corresponding author. Tel.: +33-380-380-000; fax: 33-380-380-001. E-mail address: [email protected]

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer review by the scientific conference committee of SolarPACES 2014 under responsibility of PSE AG doi: 10.1016/j.egypro.2015.03.014 Q. Lancereau et al. / Energy Procedia 69 ( 2015 ) 116 – 125 117 relatively low land requirement [1–4]. This is partly due to the commonly established weak wind load on the primary reflectors and the receiver [5,6]. Unlike for heliostats and Parabolic Trough collectors, for which many studies have been published [7–12], there is little information to be found in the literature regarding the impact of wind loads on Linear Fresnel Reflectors. Nevertheless, the wind effect on the Fresnel technology is one of the main design stresses for the metallic structure, primary reflectors, receivers and solar tracking system. Therefore, it is one of the key input elements to find the technical and economic optimum of most of the solar field parameters. The wind influences the optimum size of the primary reflectors, the spacing between the mirror lines and between the modules, the height of the receiver and the receiver aperture, and thus needs to be quantified as a function of these parameters. A LFR module with an air-stable absorber tube receiver (with protective cover glass) has been studied to determine its wind load characteristics. The drag, lift and momentum coefficients of the receiver and primary reflectors have been calculated using a bi-dimensional CFD model based on the COMSOL Multiphysics® software. The impact of the wind speed has been studied. Moreover, the interaction between the receiver and the primary reflectors has been quantified. Finally, a comparison with Parabolic Trough collectors has been made, considering an equal aperture area.

Nomenclature

Symbols

[݋(ݖ) =1 orography factor [13ܿ ܥெ௬,௥ and ܥெ௬,௠௜ momentum coefficient of the receiver and of the mirror number i [ݖ) roughness factor [13)ݎܿ ܥ௫,௥ ܥ௫,௠௜ drag coefficient of the receiver and of the mirror number i ܥ௭,௥ ܥ௭,௠௜ lift coefficient of the receiver and of the mirror number i Dr receiver diameter (m) (see Fig. 1) dlm gap between two (m) ݁ሬሬሬሬ௫Ԧ and ሬ݁ሬሬ௭Ԧ unit vector of the x and z coordinates ݂ሬሬሬ௥Ԧ and ሬ݂ሬ௠పሬሬሬԦ stress vector per unit surface applied to the receiver and the mirror number i (N/m²) ܨ௥,௫ and ܨ௠௜,௫ total stress per unit length applied to the receiver and the mirror number i (N/m) hr altitude of the receiver above the mirror plane (m) (see Fig. 1) hm altitude of the mirror plane above the soil (m) (see Fig. 1) ܫ Ӗ identity matrix ௩(ݖ) turbulence intensityܫ 2 k and ݇௘(ݖ) turbulence kinetic energy (m²/s ) and turbulence kinetic energy at the inlet boundary lm mirrors’ width ܯ௥,௬, ܯ௠௜,௬ momentum of the receiver at the center of the half-cylinder and of the mirror number i at its rotation point (N.m/m) ݊ሬԦ unit vector normal to the boundary and oriented towards the flow inlet nm = 12 number of mirrors per section of the studied Fresnel module 3 ܲ௞ turbulence kinetic energy production rate (kg/(m s )) Re and Ree10 the Reynolds number and a Reynolds number based on the velocity at the inlet and 10 meter of altitude from the soil (ݑሬԦ velocity vector of the flow (m/s ሬuሬሬሬதԦ tangential velocity vector (m/s) ܸ௕ = 28 m/s basic wind velocity for the north east of Corsica [13,14] (௠(ݖ) horizontal velocity at the inlet boundary (m/sܸ x horizontal coordinate in the study plan ݔԦ௥௜ position vector of rotation point of the mirror number i y horizontal coordinate normal to the study plan z vertical coordinate [ݖ଴ =0.005 m roughness length [13 118 Q. Lancereau et al. / Energy Procedia 69 ( 2015 ) 116 – 125

[ݖ௠௜௡ =1 m minimum height [13

Greek letters

Įmi angle of the mirror number i from the horizontal plane, counted counterclockwise 3 3 ߝ and ɂୣ(z) turbulence dissipation rate (m²/s ) and turbulence dissipation rate at the inlet boundary (m²/s ) ߢ௩ =0.41 dimensionless turbulence model parameter ିହ ߤ =1.81 10 (Pa.s) , ߤ் dynamic viscosity of the air (Pa.s), turbulent dynamic viscosity (Pa.s) ߩ = 1.225 kg/m3 density of the air (kg/m3)

Subscripts

a quantity averaged on the mirrors r receiver quantity d for the bottom or right side quantity e inlet boundary quantity i number of the mirror increasing in the direction of the flow m mirror quantity u for the upper or left side quantity x quantity according to x-coordinate y quantity according to y-coordinate z quantity according to z-coordinate

2. Presentation of the model

For this study, a two-dimensional steady-state model using a “k-H” turbulent flow has been implemented in the Comsol Multiphysics® software. The geometry study has been limited to a section of a simplified linear Fresnel module.

2.1. Geometry study

As presented in Fig. 1, twelve flat mirrors of width lm without thickness nor holder were considered. The gap between mirrors is noted dlm and their rotation axes are all aligned in a plane at altitude hm from the ground. Their angles from the horizontal plane, noted Įmi (counterclockwise), are coupled, so that the primary reflectors focus the onto the receiver. This latter is considered as a half-cylinder of diameter Dr with its flat face horizontal and facing the mirrors. The air volume under consideration is inside a rectangle with the soil at the bottom, the wind inlet boundary on the left side, the outlet boundary on the right side and an open boundary at the top. The distances between the Fresnel module and these last three boundaries are chosen so as not to influence the wind load on the receiver and mirrors, while minimizing the calculation time.

2.2. Physical model

2.2.1. Field equations In the studied field the air velocity vector ݑሬԦ and the pressure p, the turbulence kinetic energy k (m²/s²) and the turbulence dissipation rate ߝ (m²/s3) are determined solving the classical k- ߝ turbulent model, with ߤ = ିହ 3 1.81 10 Pa.s the air dynamic viscosity, ߩ. =1225 kg/m the air density, ߤ் the turbulent dynamic viscosity (Pa.s) and

் ଶ ଶ ଶ (ߤ ቂߘധݑሬԦ: ቀߘധݑሬԦ + ൫ߘധݑሬԦ൯ ቁെ ൫ߘሬԦ ήݑሬԦ൯ ቃെ ߩ݇ߘሬԦ ήݑሬԦ (1 = ܲ ௞ ் ଷ ଷ Q. Lancereau et al. / Energy Procedia 69 ( 2015 ) 116 – 125 119 the production of turbulence kinetic energy.

Fig. 1. Geometry studied and its geometrical parameters

2.2.2. Boundary conditions The inlet velocity is determined with the Eurocode for structural sizing [13,14] in Corsica where the R&D project LFR500 and the CSP plant Alba Nova 1 are under erection [15]:

(ݑ௫(ݖ) = ܸ௠(ݖ) = ܿ௥(ݖ) ܿ௢(ݖ) ܸ௕ and ݑ௭ =0, (2

with ܿ௢(ݖ) =1 the orography factor for a horizontal soil, ܸ௕ = 28 m/s the Corsica basic wind velocity and ܿ௥(ݖ) the roughness factor

0.07 ݖ0 ௭ ൬ ൰ ln ቀ ቁ for ݖ > ݖ݉݅݊ 0.19ۓ ݖ0 ܫܫ,ݖ0 (ݖ) = 0.07 , (3)ݎܿ ݖ0 ݖ݉݅݊ ۔ ൬ ൰ ln ቀ ቁ for ݖ ൑ ݖ݉݅݊ 0.19 ݖ0 ܫܫ,ݖ0 ە

with ݖ଴ = 0.005 m the roughness length, ݖ଴,ூூ = 0.05 m a reference length [13] and ݖ௠௜௡ =1 m the minimum height due to the proximity of the sea for the two projects under consideration. The turbulence kinetic energy at the inlet boundary, kୣ, is determined as follows:

ଶ (௩(ݖ) ܸ௠(ݖ)൯ , (4ܫ௘(ݖ) =1.5൫݇ with I୴(z) the turbulence intensity

ଵ ೥ if ݖ > ݖ௠௜௡ ௖బ ௟௡ቀ ቁ ೥బ (௩(ݖ) = ൞ ଵ , (5ܫ ೥೘೔೙ if ݖ ൑ݖ௠௜௡ ௖బ ௟௡ቀ ቁ ೥బ and the turbulence dissipation rate at the inlet ɂୣ is determined as follow: 120 Q. Lancereau et al. / Energy Procedia 69 ( 2015 ) 116 – 125

(ߝ௘(ݖ) = ܲ௞(ݑሬԦ = ܸ௠(ݖ)݁Ԧ௫)/ߩ (6

At the outlet boundary, the total stress is controlled to be inferior to the relative pressure (fixed at zero Pa) and an open boundary was chosen for the turbulence kinetic energy and the turbulence dissipation rate. Similarly, the top boundary was chosen to have a total stress equal to zero, and an open boundary for the turbulence kinetic energy and the turbulence dissipation rate in case of an outward flow or fixed values identical to the inlet boundary in case of an inward flow. The wall boundaries (ground and receiver) are fixed according to:

ധ ധ ் ଶ ሬԦ Ӗ ଶ Ӗ |௨ሬሬሬሬሬഓԦ| (ቃή݊ሬԦ = െߩ శ ݑሬሬሬሬఛԦ (7ܫെ ߩ݇ ܫݑሬԦή݊ሬԦ =0,ቂ(ߤ + ߤ்) ቀߘݑሬԦ + ൫ߘݑሬԦ൯ ቁെ (ߤ + ߤ்)൫ߘ ήݑሬԦ൯ ଷ ଷ ఋೢ

మ ሬԦ ఘ஼ഋ௞ ߘ݇ =0 and ߝ = శ (8) ఑ೡఋೢఓ

.with Nv = 0.4 a classical dimensionless turbulence model parameter and ݑሬሬሬሬఛԦ the tangential speed vector The boundary condition of the mirror is the same as the wall boundary for the receiver, but all variables are determined twice, for each side of the mirror. The variables are subscripted u for the upper or left side and subscripted d for the bottom or right side.

2.3. Numerical resolution

To solve the equations numerically, the geometry was discretized with a mesh totaling 0.3 million elements.

2.4. Results calculated

2.4.1. Dimensional results To determine the wind load on the mirror number i, its surface stress, noted ݂ሬሬ௠పሬሬሬԦ, was calculated from the pressure, the viscous stress and the turbulence kinetic energy:

݂ሬሬ௠పሬሬሬԦ = ݂௠௜,௫݁Ԧ௫ + ݂௠௜,௭݁Ԧ௭, (9)

் ଶ ଶ ቃӖ ሬ݊Ԧ ή݁Ԧܫ ݇ Ӗ െ ߩܫݓ݅ݐ݄ ݂ = (݌ െ݌ )൫ሬ݊Ԧ ή݁Ԧ ൯ + ቂ(ߤ + ߤ ) ቀߘധݑሬԦ + ൫ߘധݑሬԦ ൯ ቁെ (ߤ + ߤ )൫ߘሬԦ ήݑሬԦ ൯ ௠௜,௫/௭ ௨ ௗ ௫/௭ ௨ ்௨ ௨ ௨ ଷ ௨ ்௨ ௨ ଷ ௨ ௨ ௫/௭ (10) ் ଶ ଶ ቃӖ ሬ݊Ԧ ή݁Ԧܫ ݇ Ӗ െ ߩܫെቂ(ߤ + ߤ ) ቀߘധݑሬԦ + ൫ߘധݑሬԦ ൯ ቁെ (ߤ + ߤ )൫ߘሬԦ ήݑሬԦ ൯ ௗ ்ௗ ௗ ௗ ଷ ௗ ்ௗ ௗ ଷ ௗ ௗ ௫/௭

with ሬnԦ the unit vector normal to the boundary and oriented towards the inlet boundary. The total strength per unit length applied on mirror number i, noted ܨ௠௜,௫ along the x-coordinate and ܨ௠௜,௭ along the z-coordinate, can be deduced as follows:

= ݂ and = ݂ , (11) ݈݀ ௠௜,௭ ׬௠௜௥௥௢௥ ௜ ݉݅,ݖܨ ݈݀ ௠௜,௫ ׬௠௜௥௥௢௥ ௜ ݉݅,ݔܨ

and the momentum of the mirror number i at its rotation point can be calculated by this formula:

= ሬ݂ሬሬሬሬԦ ( ) ή݁ (12) ݈݀ ݔԦെݔԦ௥௠ ቁ Ԧݕ ٿ݅݉ ௠௜,௬ ׬௠௜௥௥௢௥ ௜ ቀܯ

with ሬxԦ௥௜ = (i െ 1)(l୫ +dl୫)ሬeԦ୶+h୫ሬeԦ୸ the position vector of the rotation point of the mirror number i. Similar equations are applied to the receiver:

ሬ݂ሬሬ௥Ԧ = ݂௥,௫݁Ԧ௫ + ݂௥,௭݁Ԧ௭ (13) Q. Lancereau et al. / Energy Procedia 69 ( 2015 ) 116 – 125 121

் ଶ ଶ (ቃӖ ሬ݊Ԧ ή݁Ԧ (14ܫӖ െ ߩ݇ܫ݌൫ሬ݊Ԧ ή݁Ԧ ൯ + ቂ(ߤ + ߤ ) ቀߘധݑሬԦ + ൫ߘധݑሬԦ൯ ቁെ (ߤ + ߤ )൫ߘሬԦ ήݑሬԦ൯ = ݂ ௥,௫/௭ ௫/௭ ் ଷ ் ଷ ௫/௭

= ݂ and = ݂ (15) ݖ݈݀,ܿ ݂݁ܿܽݎݑݏ ݎݒ݁݅݁ܿ݁ݎ௥,௭ ׯܨ ݔ݈݀,ܿ ݂݁ܿܽݎݑݏ ݎݒ݁݅݁ܿ݁ݎ௥,௫ ׯܨ

= ݂ሬሬሬԦ ( ) ή݁ (16) ݈݀ ݔԦെݔԦ௥௖ ቁ Ԧݕ ٿܿ ቀ ݂݁ܿܽݎݑݏ ݎݒ݁݅݁ܿ݁ݎ௖,௬ ׯܯ

(݊ െ1)(݈ +݈݀ ) .with ݔԦ = ݉ ݉ ݉ ݁Ԧ + ( ݄ + ݄ )݁Ԧ the position vector of the center of the half cylinder receiver ௥௖ 2 ݔ ௠ ௥ ݖ

2.4.2. Dimensionless results The wind load dimensionless coefficients for the drag (ܥ௫,௠௜), lift (ܥ௭,௠௜) and momentum (ܥெ௬,௠௜) of mirror number i are defined as follows:

ி೘೔,ೣ ி೘೔,೥ ெ೘೔,೤ ܥ௫,௠௜ = భ , ܥ௭,௠௜ = భ , ܽ݊݀ ܥெ௬,௠௜ = భ ൬ ௟ ఘ௏మ (௭ୀ௛ )൰ ൬ ௟ ఘ௏మ (௭ୀ௛ )൰ ൬ ௟మ ఘ௏మ (௭ୀ௛ )൰ మ ೘ ೘ ೘ మ ೘ ೘ ೘ మ ೘ ೘ ೘

In the same way, wind load dimensionless coefficients of the receiver are defined as follows:

ி೎,ೣ ி೎,೥ ெ೎,೤ ܥ = , ܥ = ܽ݊݀ ܥ = (17) ௫,௖ భವ೎ మ ௭,௖ భವ೎ మ ெ௬,௖ మ ൬ ఘ௏ (௭ୀ ௛ ା ௛ )൰ ൬ ఘ௏ (௭ୀ ௛ ା ௛ )൰ భ ವ೎ మ మ ೘ ೘ ೝ మ మ ೘ ೘ ೝ ൭ ቀ ቁ ఘ௏మ (௭ୀ௛ ା௛ )൱ మ మ ೘ ೘ ೝ

For a better comparison with Parabolic Troughs, it is interesting to calculate the average value (subscript a) of the dimensionless coefficients of the mirrors to determine the link between the total wind load and the aperture.

σ ி σ ஼ σ ி σ ஼ భರ೔ರ೙೘ ೘೔,ೣ భರ೔ರ೙೘ ೣ,೘೔ భರ೔ರ೙೘ ೘೔,೥ భರ೔ರ೙೘ ೥,೘೔ ܥ௫,௠௔ = భ = ܽ݊݀ ܥ௭,௠௔ = భ = (18) ௡ ௟ ఘ௏మ (௭ୀ௛ ) ௡ ௡ ௟ ఘ௏మ (௭ୀ௛ ) ௡ మ ೘ ೘ ೘ ೘ ೘ మ ೘ ೘ ೘ ೘ ೘

σ ெ σ ஼ భರ೔ರ೙೘ ೘೔,೤ భರ೔ರ೙೘ ಾ೤,೘೔ ܥெ௬,௠௔ = భ = (19) ௡ ௟మ ఘ௏మ (௭ୀ௛ ) ௡ మ ೘ ೘ ೘ ೘ ೘

3. Results

Fig. 2 shows the Reynolds number (Re) for the first mirror having an angle of -45°.

ఘ|௨ሬሬԦ| ௟೘ ܴ݁ = (20) ఓ

As is commonly admitted for most angle positions, the first mirror is the most exposed to the wind load and the other mirrors are more protected and are only subjected to secondary flows which magnitude is less important than the main flow. The receiver is quite exposed to the wind load, but thanks to its wing-like shape and its small dimensions, it does not perturb the main flow. To study the influence of the wind velocity, some calculus has been done for other basic wind velocities (Vb) and another Reynolds number based on the inlet velocity at 10 meters of altitude from the soil (Ree10) was defined:

ఘ ௏೘(௭ ୀ ଵ଴௠) ௟೘ ܴ݁ = (21) ௘ଵ଴ ఓ 122 Q. Lancereau et al. / Energy Procedia 69 ( 2015 ) 116 – 125

Fig. 2. Dimensionless velocity (Re) and streamline for an angle of the first mirror Dm1 = -45°

Fig. 3 shows no influence of the Reynolds number, for the studied range, on the momentum coefficient of the receiver. The draft and lift coefficients are respectively weakly increasing and decreasing with the increase of the Reynolds number. It is due to the evolution of the size of the secondary flow downstream of the receiver. Fig. 4 shows no influence of the Reynolds number, for the studied range, on the drag, lift and momentum coefficients of the first mirror. These results can also be generalized to other mirrors. Therefore, the next results on the mirrors are only presented for the basic wind velocity for the north east of Corsica ܸ௕ = 28 m/s [13,14]. Fig. 5 shows the influence of the first mirror angle on the drag, lift and momentum coefficients of the first mirror. The drag coefficient is between 2.5 and 0, the lift coefficient is between -1.25 and 1.25 and the momentum is between -0.12 and 0.1. For the other mirrors, Fig. 6 shows that the drag and lift coefficients are of much less importance than for the first mirror, for most of the first mirror angle range. The only exception is for Dm1 = 0° where the first mirror does not protect the other mirrors from the wind. For the momentum coefficient, as the wind load does not generate an important torque, the reduction for the other mirrors is less important. This reduction is significant for Dm1 = -110° and -45°, but for Dm1 = 0° a small increase can be observed from the first mirror to the fifth. More globally, Fig. 7 shows that the average drag and lift are much smaller than if only the first mirror was taken into account. Thus, the structure sizing should take into account the wind load of all mirrors, in order not to oversize. Moreover, the average momentum coefficient is much smaller than for the first mirror: this shows the interest to have a tracking system coupling the different mirrors, to average the torque and thus reduce the consumption.

Q. Lancereau et al. / Energy Procedia 69 ( 2015 ) 116 – 125 123

Fig. 3. Drag, lift and momentum coefficients of the receiver (respectively Cx,r, Cz,r and CMy,r) as a function of Ree10.

Fig. 4. Drag, lift and momentum coefficients of the first mirror (respectively Cx,m1, Cz,m1 and CMy,m1) as a function of Ree10, for two different angles of the first mirror: Dm1 = 90° (left figure) and Dm1 = 45° (right figure).

Fig. 5. Drag, lift and momentum coefficients of the first mirror (respectively Cx,m1, Cz,m1 and CMy,m1) as a function of the first mirror angleDm1. 124 Q. Lancereau et al. / Energy Procedia 69 ( 2015 ) 116 – 125

Fig. 6. Drag, lift and momentum coefficients of the mirrors (respectively Cx,mi, Cz,mi and CMy,mi) as a function of the number of the mirror i for different first mirror angles Dm1.

Fig. 7. Average drag, lift and momentum coefficients of the mirrors (respectively Cx,ma, Cz,ma and CMy,ma) as a function of the first mirror angle Dm1. Q. Lancereau et al. / Energy Procedia 69 ( 2015 ) 116 – 125 125

4. Comparison with Parabolic Trough

The Parabolic Trough technology has been chosen for comparison because it is the most mature CSP technology, and as for the LFR technology, uses single-axis tracking. For an isolated Parabolic Trough collector without torque tube, the drag, lift and momentum coefficients are respectively around 1, 0.5 and 0.6 according to Mier-Torrecilla’s study [16] and around 2, 2 and 0.2 according to Hosoya’s study [17] for the worse position. Thus, according to the results previously presented, for the same aperture, the drag, lift and torque applied to the mirrors of a LFR module are respectively around 5 to 10 times, 1.2 to 8 times and 50 to 150 times lower than for the Parabolic Trough module. With the low drag and lift, and a lower mirror altitude, an important cost reduction of the structure can be reached. The very important difference for the torque can be explained by the important difference of the lever length (proportional to the single mirror width for the Fresnel and to the total aperture for the Parabolic Trough), which introduces the number of Fresnel mirrors as a factor between the momentum coefficients of Fresnel and Parabolic Trough technologies. Consequently to the low torque, a much lower power consumption is expected for the Fresnel technology compared to the Parabolic Trough technology, as well as a reduction in the cost of the mirror holders and tracking system.

5. Conclusion

This study characterized the wind load of the Fresnel technology for a given configuration, which allowed to quantify the interest of this technology when compared to the Parabolic Trough technology, in terms of wind loads. Ongoing work consists in a parametric study using the parameters defined in this first paper, in order to determine the most relevant parameters in studying wind loads for the Fresnel technology. Moreover, a further investigation will establish the influence of a complete solar field, including several lines of LFR collectors. All these results will be further compared in another study through pressure and wind speed measurements on a full- scale Linear Fresnel Reflector prototype.

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